Air carrier pilot reported while flying an RNAV approach to SLC they descended below charted altitude and ATC issued a low altitude alert. The flight crew climbed; rejoined the glide path; and landed safely.

Narrative

Cleared for a visual approach to RW 35 in SLC from waypoint HLMET. I chose and briefed the RNAV (GPS) Rwy 35 as a backup; and to practice my RNAV approach procedures as the LDA 35 was not in the navigation database. I was fully configured for landing at the final approach fix (FAF) KERNN at 6100 ft MSL. Waypoint WEEEL was not in the database; but I did brief that it was 1.9 miles from the end of the runway; and that it was required to track the approach course to wheel before turning to align with the landing runway; which is a 5.05 degree offset. Maybe because WEEEL was not in the database; I began a 1000-1200 fpm descent to the LNAV Cat C minimums at the FAF; thus going below the at or above 4900 altitude at WEEEL. We received an altitude alert from the Tower. I disconnected the autopilot and began a climb to visually transition to the PAPI lights; which were in view throughout the final approach. I told myself in my head; and even verbalized to an inquiring FO; that we were low on the PAPI lights because we were still short of the Visual Descent Point (VDP); which is located .9 miles from the end of the runway. I subsequently re-established a proper approach path and runway alignment and an uneventful landing. Crew Errors: 1). At the FAF; 4900 feet should have been selected until passing WEEEL where a descent to minimums could be initiated. Both pilots failed to notice this oversight.2). Since we were at or below 500 feet AGL and not on a normal approach path for landing; a go around should have been called for by either pilot; and initiated by the CA who was the pilot flying. From the FAF; I could have very easily tracked the course to WEEEL and just followed the PAPI lights as they were clearly in sight; but I wanted to practice a simulated LNAV approach. Missing the 4900 foot restriction at WEEEL lead to the approach path deviations. Also; since we were cleared for a visual approach; we could have used the LDA 35 as a backup to the visual approach with course and glide path guidance (green needles). Lessons learned: Don't hesitate to go around if the approach doesn't look right or if stabilized approach criteria are not met. Also; make sure that all of the PM calls are made which require a PF response and can be used to trap errors. Cause: Failure to maintain a minimum altitude (4900 at WEEEL) inside the final approach fix. Failure as a crew to verify that the requested VNAV altitude was selected.Suggestions: Especially in VFR conditions and cleared for a visual approach; use ALL available resources to maintain proper course and path. Strict adherence to company Standard Operating Procedures.